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ArcCosh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCosh[z] > Transformations > Products, sums, and powers of the direct function > Differences of the direct function





http://functions.wolfram.com/01.26.16.0159.01









  


  










Input Form





ArcCosh[x] - ArcCosh[y] == ArcSinh[ (-1)^Floor[1/2 - Arg[(-x) y + Sqrt[-1 + x] Sqrt[1 + x] Sqrt[-1 + y] Sqrt[1 + y]]/Pi] ((-Sqrt[-1 + x]) Sqrt[1 + x] y + x Sqrt[-1 + y] Sqrt[1 + y])] + (1/2) Pi ((((1/2) I)/(-1)^Floor[-(Arg[1 - x]/(2 Pi))] + ((1/2) I)/(-1)^Floor[-(Arg[1 - y]/(2 Pi))]) (-1 + (-1)^Floor[1/2 - Arg[x y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi] + 2 (-1 + (-1)^Floor[1/2 - Arg[x y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi]) Floor[(Arg[I x + Sqrt[1 - x^2]] + Arg[(-I) y + Sqrt[1 - y^2]])/ (2 Pi)] + 2 (1 + (-1)^Floor[1/2 - Arg[x y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi]) Floor[1/2 - (Arg[I x + Sqrt[1 - x^2]] + Arg[(-I) y + Sqrt[1 - y^2]])/ (2 Pi)]) + (((1/2) I)/(-1)^Floor[-(Arg[1 - x]/(2 Pi))] - ((1/2) I)/(-1)^Floor[-(Arg[1 - y]/(2 Pi))]) (1 + (-1)^Floor[1/2 - Arg[(-x) y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi] + 2 (-1 + (-1)^Floor[1/2 - Arg[(-x) y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi]) Floor[(Arg[I x + Sqrt[1 - x^2]] + Arg[I y + Sqrt[1 - y^2]])/(2 Pi)] + 2 (1 + (-1)^Floor[1/2 - Arg[(-x) y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi]) Floor[1/2 - (Arg[I x + Sqrt[1 - x^2]] + Arg[I y + Sqrt[1 - y^2]])/ (2 Pi)]))










Standard Form





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MathML Form







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/> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> x </ci> <ci> y </ci> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <floor /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <arg /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> x </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <arg /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





© 1998- Wolfram Research, Inc.